Review pubs.acs.org/CR
Modeling Molecular Interactions in Water: From Pairwise to ManyBody Potential Energy Functions Gerardo Andrés Cisneros,† Kjartan Thor Wikfeldt,‡,§ Lars Ojamaë ,# Jibao Lu,∥ Yao Xu,⊥ Hedieh Torabifard,† Albert P. Bartók,@ Gábor Csányi,@ Valeria Molinero,∥ and Francesco Paesani*,∇ †
Department of Chemistry, Wayne State University, Detroit, Michigan 48202, United States Science Institute, University of Iceland, VR-III, 107, Reykjavik, Iceland § Department of Physics, Albanova, Stockholm University, S-106 91 Stockholm, Sweden ∥ Department of Chemistry, The University of Utah, Salt Lake City, Utah 84112-0850, United States ⊥ Lehrstuhl Physikalische Chemie II, Ruhr-Universität Bochum, 44801 Bochum, Germany @ Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB21PZ, United Kingdom # Department of Chemistry, Linköping University, SE-581 83 Linköping, Sweden ∇ Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States ‡
ABSTRACT: Almost 50 years have passed from the first computer simulations of water, and a large number of molecular models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of analytical potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approximations and on their ability to accurately reproduce reference data obtained from state-of-the-art electronic structure calculations and experimental measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a physically correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought “universal model” capable of describing the behavior of water under different conditions and in different environments.
CONTENTS 1. Introduction 2. Many-Body Expansion of the Interaction Energy 3. Pairwise Additive Analytical Potential Energy Functions 4. Many-Body Analytical Potential Energy Functions 4.1. Implicit Many-Body Potential Energy: Empirical Models 4.2. Implicit Many-Body Potential Energy: Polarizable Models 4.3. Explicit Many-Body Potential Energy 5. Conclusions and Future Directions Author Information Corresponding Author Notes Biographies Acknowledgments References
providing fundamental insights that are otherwise difficult to obtain by other means. However, both the realism and the predicting power of a computer simulation directly depend on the accuracy with which the molecular interactions and the overall system dynamics are described. Rigorously, realistic computer simulations of water should include an accurate representation of the underlying Born−Oppenheimer potential energy surface (PES) in combination with a proper treatment of the nuclear motion at a quantum-mechanical level.1−3 Along these lines, different theoretical and computational approaches have been proposed, which can be conveniently separated in two main groups depending on how the water PES is described. The first group includes simulation approaches that use a set of predefined analytical functions to represent the underlying PES of the water system of interest as a function of the corresponding molecular coordinates. These analytical potential energy functions are historically referred to as “force fields”.4−8 The second group includes the so-called “ab initio” approaches in which the water PES is obtained “on the fly” by performing
7501 7502 7505 7506 7506 7508 7511 7519 7520 7520 7520 7520 7520 7521
Special Issue: Water - The Most Anomalous Liquid
1. INTRODUCTION Computer simulations have become an indispensable tool for characterizing the properties of water at the molecular level, often © 2016 American Chemical Society
Received: October 31, 2015 Published: May 17, 2016 7501
DOI: 10.1021/acs.chemrev.5b00644 Chem. Rev. 2016, 116, 7501−7528
Chemical Reviews
Review N
quantum-chemical calculations to solve the electronic timeindependent Schrö dinger equation for a given molecular configuration.9−14 Ab initio approaches can be further distinguished in methods based on wave function theory (WFT) and density functional theory (DFT). Independent of how the water PES is represented, the nuclear dynamics can then be described at the classical level using Newton’s equations of motion or at the quantum-mechanical level by solving the corresponding nuclear time-dependent Schrödinger equation using grid methods, wave packets, semiclassical approaches, and methods built upon Feynman’s path-integral formalism.15−21 As part of this thematic issue “Water - The Most Anomalous Liquid”, this article reviews recent progress in the development and application of analytical potential energy functions (PEFs) that aim at correctly representing many-body effects in water from the gas to the liquid phase. Specific focus is on different classes of PEFs built upon a hierarchy of approximate representations of many-body effects and on their ability to accurately reproduce reference data obtained from state-of-theart (i.e., correlated) electronic structure calculations. With this objective in mind, we introduce and describe the many-body expansion (MBE) of the interaction energy in section 2. Purely pairwise PEFs are only briefly mentioned in section 3, while different classes of many-body PEFs are described in section 4. Within each class, the accuracy of the individual PEFs is assessed systematically through the analysis of the energetics of water clusters for which correlated electronic structure calculations are possible. To determine how the accuracy of each PEF in representing the fundamental interactions between water molecules translates into the ability of the same PEF to reproduce measurable quantities, comparisons with experimental data for representative structural, thermodynamic, and dynamical properties of liquid water are also discussed. Although the ability to correctly reproduce the experimental data is the ultimate goal of a computer simulation, “getting the right results for the right reasons” is even more important for the correct interpretation of the underlying molecular mechanisms. We will show that the apparent perfect agreement with the results of experimental measurements that are mainly sensitive to the average molecular behavior is often the result of error cancellation between different many-body contributions to the total interaction energy. These deviations from the actual Born− Oppenheimer PES effectively preclude a rigorous and quantitative interpretation of the experimental measurements, which has led, in the past, to the proliferation of water models. As discussed in section 4, the advent of explicit many-body PEFs holds great promise for a physically correct, molecular-level description of the properties of water across different phases. Building upon recent achievements and, in several cases, unprecedented accuracy of many-body PEFs, future development and applications to aqueous systems are presented in section 5.
VN (r1, ..., rN ) =
N
∑ V1B(r)i + ∑ V2B(ri, rj) i=1
i
